What's fundamental for quantum mechanics?

As I understand it, a lot of what is taught about quantum mechanics are special techniques for solving problems. I'm not a physicist, so something like perturbation theory is not what I'm after. To be more specific, i would like to know the minimum that is necessary for "doing" quantum mechanics, regardless of how inefficient it would be to apply these minimal techniques to complex problems (because as a non-physicist I will never have to work out a complex problem).

What I have learned so far is that the Schrodinger equation is not enough because it does not take spin into account. I think the Schrodinger-Pauli and Dirac equations do. Are there any other equations I should look up? Are knowing the equations and how to apply Hamiltonians all that is really necessary for working out any QM problem (regardless of how time-consuming it would be)?

The "minimum" would depend on what kind of problem(s) you are interested in. The great divide in applied QM is between solid state (including surface) applications and molecular (including cluster) applications.

As I understand it, a lot of what is taught about quantum mechanics are special techniques for solving problems. I'm not a physicist, so something like perturbation theory is not what I'm after. To be more specific, i would like to know the minimum that is necessary for "doing" quantum mechanics, regardless of how inefficient it would be to apply these minimal techniques to complex problems (because as a non-physicist I will never have to work out a complex problem).

What I have learned so far is that the Schrodinger equation is not enough because it does not take spin into account. I think the Schrodinger-Pauli and Dirac equations do. Are there any other equations I should look up? Are knowing the equations and how to apply Hamiltonians all that is really necessary for working out any QM problem (regardless of how time-consuming it would be)?